Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-3x+3y &= -1 \\ 6x+6y &= -9\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $6x = -6y-9$ Divide both sides by $6$ to isolate $x$ $x = {-y - \dfrac{3}{2}}$ Substitute this expression for $x$ in the first equation. $-3({-y - \dfrac{3}{2}}) + 3y = -1$ $3y + \dfrac{9}{2} + 3y = -1$ Simplify by combining terms, then solve for $y$ $6y + \dfrac{9}{2} = -1$ $6y = -\dfrac{11}{2}$ $y = -\dfrac{11}{12}$ Substitute $-\dfrac{11}{12}$ for $y$ in the top equation. $-3x+3( -\dfrac{11}{12}) = -1$ $-3x-\dfrac{11}{4} = -1$ $-3x = \dfrac{7}{4}$ $x = -\dfrac{7}{12}$ The solution is $\enspace x = -\dfrac{7}{12}, \enspace y = -\dfrac{11}{12}$.